R(x)=100x-0.5x^2

Solution for R(x)=100x-0.5x^2 equation:

(R)=100R-0.5R^2

We move all terms to the left:

(R)-(100R-0.5R^2)=0

We get rid of parentheses

0.5R^2-100R+R=0

We add all the numbers together, and all the variables

0.5R^2-99R=0

a = 0.5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·0.5·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*0.5}=\frac{0}{1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*0.5}=\frac{198}{1}
=198
$